Vol. 37

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2014-06-16

Magnitude Constraint Minimum Variance Beamformer with Conjugate Symmetric Constraint and Norm Constraint

By Lulu Zhao, Guang Liang, and Huijie Liu
Progress In Electromagnetics Research M, Vol. 37, 41-50, 2014
doi:10.2528/PIERM14042808

Abstract

In this paper, an improved robust minimum variance beamformer against direction of arrival (DOA) mismatch and finite sample effect is proposed. Multiple inequality magnitude constraints are imposed to broaden the main lobe of beampattern. The conjugate symmetric structure of the optimal weight is utilized to transform the non-convex inequality magnitude constraints into convex ones. A quadratic constraint on the norm of weight is introducing to make further improvement on robustness against DOA mismatch and finite sample effect. The proposed beamforming problem can be reformulated in the form of the second order cone programming and solved efficiently by interior point method. Simulation results show that the proposed beamformer outperforms several other adaptive beamformers.

Citation


Lulu Zhao, Guang Liang, and Huijie Liu, "Magnitude Constraint Minimum Variance Beamformer with Conjugate Symmetric Constraint and Norm Constraint," Progress In Electromagnetics Research M, Vol. 37, 41-50, 2014.
doi:10.2528/PIERM14042808
http://www.jpier.org/PIERM/pier.php?paper=14042808

References


    1. Van Veen, B. D. and K. M. Buckley, "Beamforming: A versatile approach to spatial filtering," IEEE Acoust., Speech, Signal Process. Mag., Vol. 5, No. 2, 4-24, 1988.

    2. Godara, L. C., "Application of antenna arrays to mobile communications, Part II: Beam-forming and direction-of-arrival considerations," Proc. IEEE, Vol. 85, No. 8, 1195-1245, 1997.
    doi:10.1109/5.622504

    3. Qu, Y., G. S. Liao, S. Q. Zhu, and X. Y. Liu, "Pattern synthesis of planar antenna array via convex optimization for airborne forward looking radar," Progress In Electromagnetics Research, Vol. 84, 1-10, 2008.
    doi:10.2528/PIER08060301

    4. Capon, J., "High-resolution frequency-wavenumber spectrum analysis," Proc. IEEE, Vol. 57, No. 8, 1408-1418, 1969.
    doi:10.1109/PROC.1969.7278

    5. Wax, M. and Y. Anu, "Performance analysis of the minimum variance beamformer in the presence of steering vectors errors," IEEE Trans. Signal Process., Vol. 44, No. 4, 938-947, 1996.
    doi:10.1109/78.492546

    6. Van Trees, H. L., Detection, Estimation and Modulation Theory, Part IV: Optimum Array Processing, Wiley, New York, 2002.

    7. Carlson, B. D., "Covariance matrix estimation errors and diagonal loading in adaptive arrays," IEEE Trans. Aerosp. Electron. Syst., Vol. 24, No. 4, 397-401, 1988.
    doi:10.1109/7.7181

    8. Wax, M. and Y. Anu, "Performance analysis of the minimum variance beamformer," IEEE Trans. Signal Process., Vol. 44, No. 4, 928-937, 1996.
    doi:10.1109/78.492545

    9. Stoica, P., Z. Wang, and J. Li, "Robust Capon beamforming," IEEE Signal Process. Lett., Vol. 10, No. 6, 172-175, 2003.
    doi:10.1109/LSP.2003.811637

    10. Lorenz, R. G. and S. P. Boyd, "Robust minimum variance beamforming," IEEE Trans. Signal Process., Vol. 53, No. 5, 1684-1696, 2005.
    doi:10.1109/TSP.2005.845436

    11. Lie, J. P., W. Ser, and C. M. S. See, "Adaptive uncertainty based iterative robust Capon beamformer using steering vector mismatch estimation," IEEE Trans. Signal Process., Vol. 59, No. 9, 4483-4488, 2011.
    doi:10.1109/TSP.2011.2157500

    12. Nai, S. E., W. Ser, Z. L. Yu, and H. Chen, "Iterative robust minimum variance beamforming," IEEE Trans. Signal Process., Vol. 59, No. 4, 1601-1611, 2011.
    doi:10.1109/TSP.2010.2096222

    13. Zaharis, Z. D., C. Skeberis, and T. D. Xenos, "Improved antenna array adaptive beamforming with low side lobe level using a novel adaptive invasive weed optimization method," Progress In Electromagnetics Research, Vol. 124, 137-150, 2012.
    doi:10.2528/PIER11120202

    14. Liu, C. F. and J. Yang, "Robust LCMP beamformer with negative loading," Progress In Electromagnetics Research, Vol. 130, 541-561, 2012.
    doi:10.2528/PIER12061909

    15. Chen, Y. L. and J. H. Lee, "Finite data performance analysis of MVDR antenna array beamformers with diagonal loading," Progress In Electromagnetics Research, Vol. 134, 475-507, 2013.
    doi:10.2528/PIER12092006

    16. Yang, K., Z. Q. Zhao, and Q. H. Liu, "Robust adaptive beamforming against array calibration errors," Progress In Electromagnetics Research, Vol. 140, 341-351, 2013.
    doi:10.2528/PIER13042203

    17. Li, J., P. Stoica, and Z.Wang, "On robust Capon beamforming and diagonal loading," IEEE Trans. Signal Process., Vol. 51, No. 7, 1702-1715, 2003.
    doi:10.1109/TSP.2003.812831

    18. Vorobyov, S. A., A. B. Gershman, and Z. Q. Luo, "Robust adaptive beamforming using worst-case performance optimization: A solution to the signal mismatch problem," IEEE Trans. Signal Process., Vol. 51, No. 2, 313-324, 2003.
    doi:10.1109/TSP.2002.806865

    19. Li, J., P. Stoica, and Z. Wang, "Doubly constrained robust Capon beamformer," IEEE Trans. Signal Process., Vol. 52, No. 7, 2407-2423, 2004.
    doi:10.1109/TSP.2004.831998

    20. Booker, A. and C. Y. Ong, "Multiple constraint adaptive filtering," Geophysics, Vol. 36, No. 3, 498-509, 1971.
    doi:10.1190/1.1440187

    21. Frost III, O. L., "An algorithm for linearly constrained adaptive array processing," Proc. IEEE, Vol. 60, No. 8, 926-935, 1972.
    doi:10.1109/PROC.1972.8817

    22. Huarng, K. C. and C. C. Yeh, "Adaptive beamforming with conjugate symmetric weights," IEEE Trans. Signal Process., Vol. 39, No. 7, 926-932, 1991.

    23. Boyd, S. and L. Vandenberghe, Convex Optimization, Cambrideg University Press, Cambridge, UK, 2004.
    doi:10.1017/CBO9780511804441

    24. Cox, H., R. M. Zeskind, and M. M. Owen, "Robust adaptive beamforming," IEEE Trans. Acoust., Speech, Signal Process, Vol. 35, No. 10, 1365-1376, 1987.
    doi:10.1109/TASSP.1987.1165054

    25. Tian, Z., K. L. Bell, and H. L. Van Trees, "A recursive least squares implementation for LCMP beamforming under quadratic constraint," IEEE Trans. Signal Process., Vol. 49, No. 6, 1138-1145, 2001.
    doi:10.1109/78.923296

    26. Liu, J., A. B. Gershman, Z. Q. Luo, and K. M. Wong, "Adaptive beamforming with sidelobe control: A second-order cone programming approach," IEEE Signal Process. Lett., Vol. 10, No. 11, 331-334, 2003.
    doi:10.1109/LSP.2003.817852

    27. Strum, J. F., "Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones," Optimization Methods and Software, Vol. 11, No. 1-4, 625-653, 1999.
    doi:10.1080/10556789908805766

    28. Luenberger, D. G. and Y. Y. Ye, Linear and Nonlinear Programming, Springer, New York, 2008.